THE USE OF DIFFERENCE METHODS IN MAKING POLYNOMIAL FITS TO DISCRETE DATA
NAVAL WEAPONS LAB DAHLGREN VA
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A difference method, which for one choice of weights applied to the differences leads to equally weighted least squares polynomial fits to equally spaced data, is generalized so that the approximation can be obtained in terms of polynomials chosen by the user in the fitting of equally spaced or unequally spaced data. Using this method, an investigation was made into the ballistics field with particular emphasis on the preparation of bombing tables. The technique of using differences in making polynomial fits to discrete data is not new and has been widely discussed in the literature. However, the method described in this report enables the user to apply this method using any form of interpolating polynomial which best suits his purpose. Also, by changing from ordinary differences, which are used in working with equally spaced data, to divided differences, the method can be used for unequally spaced data. For the convenience of the user the report contains the tabulations of the multipliers, the weights and the summations of weights through the 4th difference for equally spaced data containing from 5 to 30 points. With the modification presented these weights may be adapted for use with unequally spaced data.
- Statistics and Probability